(12+x+x)(15+x+x)=550

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Solution for (12+x+x)(15+x+x)=550 equation: 


Simplifying
(12 + x + x)(15 + x + x) = 550

Combine like terms: x + x = 2x
(12 + 2x)(15 + x + x) = 550

Combine like terms: x + x = 2x
(12 + 2x)(15 + 2x) = 550

Multiply (12 + 2x) * (15 + 2x)
(12(15 + 2x) + 2x * (15 + 2x)) = 550
((15 * 12 + 2x * 12) + 2x * (15 + 2x)) = 550
((180 + 24x) + 2x * (15 + 2x)) = 550
(180 + 24x + (15 * 2x + 2x * 2x)) = 550
(180 + 24x + (30x + 4x2)) = 550

Combine like terms: 24x + 30x = 54x
(180 + 54x + 4x2) = 550

Solving
180 + 54x + 4x2 = 550

Solving for variable 'x'.

Reorder the terms:
180 + -550 + 54x + 4x2 = 550 + -550

Combine like terms: 180 + -550 = -370
-370 + 54x + 4x2 = 550 + -550

Combine like terms: 550 + -550 = 0
-370 + 54x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-185 + 27x + 2x2) = 0

Factor a trinomial.
2((-37 + -2x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-37 + -2x)' equal to zero and attempt to solve:

Simplifying
-37 + -2x = 0

Solving
-37 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '37' to each side of the equation.
-37 + 37 + -2x = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -2x = 0 + 37
-2x = 0 + 37

Combine like terms: 0 + 37 = 37
-2x = 37

Divide each side by '-2'.
x = -18.5

Simplifying
x = -18.5

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-18.5, 5}

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